create gaps between spline points with animation nodes
This answer will be using the technique described in my answer here. After getting the parameters of the intersections, we prepend it with zero and append it with 1 representing the start and end of the spline respectively. The prepended list represents the starting parameters of the sub-splines between intersection points while the appended list represents the ending parameters. We can generate those sub-splines by trimming as follows:



We can then loop over the sub-splines, evaluate a point in the middle and see if it is inside the object or not, if yes, we append the spline:



And that is it, you now have the interior splines which you can evaluate to get what you want. For instance: